Ok, assuming "mj" in the question is Megajoules MJ) you need a total amount of rotational kinetic energy in the fly wheel at the beginning of the trip that equals
(2.4e6 J/km)x(300 km)=7.2e8 J
The expression for rotational kinetic energy is
E = (1/2)Iω²
where I is the moment of inertia of the fly wheel and ω is the angular velocity.
So this comes down to finding the value of I that gives the required energy. We know the mass is 101kg. The formula for a solid cylinder's moment of inertia is
I = (1/2)mR²
We want (1/2)Iω² = 7.2e8 J and we know ω is limited to 470 revs/sec. However, ω must be in radians per second so multiply it by 2π to get
ω = 2953.1 rad/s
Now let's use this to solve the energy equation, E = (1/2)Iω², for I:
I = 2(7.2e8 J)/(2953.1 rad/s)² = 165.12 kg·m²
Now find the radius R,
165.12 kg·m² = (1/2)(101)R²,
√(2·165/101) = 1.807m
R = 1.807m
Answer:
a.) the speed at the bottom is greater for the steeperhill
Explanation:
since the energy at the bottom of the steeper hilis greater
As we can see from above that v is higher when h ishigher.
Force applied causes
deformation in the object. It changes the relative positions of
constituent particles in the crystal lattice.
As soon as that happens, the interatomic or intermolecular forces come
into play and they, tend to restore the solid back to it's original
shape.
This restoring force per unit area is called Stress . When external forces are removed, the internal forces tend to restore the solid back.
This property is called Elasticity .
However, no material is perfectly elastic and what happens is that, the body is not able to restore itself completely.
